This paper studies the posterior Cramér-Rao lower bound(PCRLB) of the mean-square error in real-time state estimation for a discrete-time system with quantized measurements in the area of networked systems. The optimal real-time reconstruction and the minimum real-time mean-square distortion function of quantization law are presented. Then the PCRLB is obtained in terms of the model of the system and the minimum real-time mean-square distortion function of the quantization law adapted in the system. The proposed PCRLB shows the quantization effect, especially the influence of the real-time mean-square distortion function on the performance of the state estimation. It is found that in the case when the system with a communication network is unstable, the PCRLB may not be bounded for a quantization law with a low bit-rate.